An intrinsic velocity dispersion of 5% has been measured from 2 to 7 kHz in a water saturated crystalline rock. The porosity of the granite is 0.008 and consists of microcracks. Specific attenuation was observed to be weakly dependent on frequency over the same band. We also measured longitudinal and shear specific attenuation as a continuous function of water saturation at 1-2 kHz. The constant-Q model inadequately describes the dispersion. The dispersion mechanism is hydrodynamic relaxation of the microcracks. An effective pressure of 10 MPa reduces the dispersion to less than 1% per decade, or 4% from 1 Hz to 1 MHz. The intrinsic dispersion is insufficient to account for the discrepancies between seismic, sonic, and ultrasonic velocities which are observed in the field. The in-situ velocity drift is a factor of four greater than the maximum intrinsic dispersion. We conclude that such a velocity drift in crystalline rocks is caused by sampling resolution of macroscopic fractures.